A protected monopoly which is unregulated makes profit by restricting
production to raise the price of its product. It makes a profit but the gain in
profit from monopolization of a market is less than the cost to consumers as a
result of the higher price. Therefore there is a net social loss from a
protected monopoly.

To prove this proposition let us start with a special historical case. In the
Middle Ages and later kings often granted a monopoly for the sale of salt to one
organization because it was easier to collect a tax on salt from one enterprise
than from the many salt producers and sellers that would exist under
competition.

The socially optimum output and price are given by the intersection of the
demand schedule and the marginal cost curve. The demand curve represents the
marginal benefit curve so the intersection corresponds to the level of
production and consumption such that marginal benefit is equal to marginal cost
and both correspond to the market price. These are represented in the above
graph by Qopt and Popt. The monopolist maximizes its profits where marginal cost
is equal to marginal revenue. In the graph the level of output of the monopolist
is shown as Qm and the price the monopolist establishes is Pm. Although the
monopolist has a monopoly on the sale of sale it does not necessarily have to
produce the salt itself. It could get the amount Qm by offering the price Pp.
The monopoly's profit would then be the difference between the price it sells
the salt and the price at which it purchases times the amount sold; i.e.,
monopoly profit equals (Pm-Pp)Qm. The level of the monopoly profit can be
compared with the loss to the consumers and the salt producers, as is shown in
the diagram below.

The loss to the consumers is the area of the pink-colored trapezoid. The loss
in producers' surplus to the salt makers is the area of the purplish-colored
trapezoid. The profit of the monopolist is the green-hatched rectangle. Clearly
the loss of consumer and producer surpluses is greater than the amount of the
monopoly profit by the area of the triangles.

If the monopolist does not purchase the quantity it sells but instead
produces it itself then the purplish colored area is the profit the monopolist
would lose in functioning as a monopolist rather than as a price-taking firm
producing at the socially optimum level of production. Thus the net gain in
profit for the monopolist is the monopoly profit less the area of the purplish
trapezoid.

The net loss of the economy due to the monopoly is the area of the pink and
purplish trapezoid less the rectangle representing the monopoly profit. The
result is the same as before; the net social loss due to the monopoly is the
area of the two triangles.

It is very important to remember that the above analysis applies only to the
protected monopoly; i.e., a firm who is protected by the State from competition.
If there is a small town which there is only a single grocery store despite
freedom of entry then that store has a monopoly but it is not a protected
monopoly. Even if that store exploits its monopoly power there is no economic
welfare loss due to monopoly. When the town grows enough it will get another store.
The town will get another store when someone sees that the revenue it will generate
exploiting
all the opportunities for price setting and discrimination will be greater than the cost.
For the people of the town it is not a choice between perfect competition and
monopoly it is a choice between mon-opoly and zero-opoly. The town's people are
clearly better off with the exploitative monopoly than they were with no store
because they can if they ignore the existence of the store and continue to do
whatever they did before the store located there.

The above point harkens back to the French engineer, Jules Dupuit, who
essentially founded cost benefit analysis. He asked when should a bridge be
built in a particular location. His answer was that it should be built when the
revenues that would be generated if the bridge were operated as a monopoly
taking advantage of price discrimination exceeds the costs of building it. In
building and operating it the costs may be reduced taking advantage of
monopsonistic advantages at the location. Dupuit did not assert that the bridge
should actually be operated that way, he was only looking for a criterion about
when or if the bridge should be built. However, any other mode of operation
would require government subsidies financed out of taxes which would involve a
transfer of welfare from one segment of the economy to another.

On this matter of possible welfare losses due to competition deemed not to be
perfect the Austrian School of Economics deviates sharply from the Neoclassical
School. Clearly in this matter the Austrian School is correct; freedom of entry
and exit is the essential criterion of competitiveness.